Abstract
The Alfvén and high frequency electromagnetic waves propagating in a relativistic two-fluid plasma influenced by the gravitational field of the Reissner–Nordström–anti-de Sitter (RNAdS) black hole have been investigated applying 3+1 split of spacetime. The extremal cases also discussed here based on the simple observation that the near-horizon geometry of a static extremal black hole contains two-dimensional anti-de Sitter factor even in the presence of positive cosmological constant. We reformulate the relativistic two-fluid equations with the set of simultaneous linear equations for the perturbations. We derive the dispersion relation for these waves and solve numerically for the wave number k.
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